Inverse mapping theorem and local forms of continuous mappings
type: Item
instance of: scholarly article
title: Inverse mapping theorem and local forms of continuous mappings
zbMATH Open document ID: 1330.55003
published in: Topology and its Applications
publication date: 2015-12-08T00:00:00Z
review text: The authors prove the following inverse mapping theorem (without any differentiability assumptions): Let \(f:X\to Y\) be an open discrete continuous mapping between two oriented topological manifolds of the same dimension and assume that \(|\text{deg}(f,x_0)|=1\) for some \(x_0\in X\). Then \(f\) is a local homeomorphism at \(x_0\).
Mathematics Subject Classification ID: 55M25
Mathematics Subject Classification ID: 58C15
Mathematics Subject Classification ID: 57N45
zbMATH DE Number: 6517538
zbMATH Keywords: local degree
zbMATH Keywords: inverse mapping theorem
zbMATH Keywords: local immersion theorem
zbMATH Keywords: local submersion theorem
author: Alexandre Paiva Barreto
author: Marcio Colombo Fenille
author: Luiz Hartmann
reviewed by: Christian Fenske
MaRDI profile type: Publication
full work available at URL: j.topol.2015.10.013
OpenAlex ID: W2145130915
cites work: The implicit function theorem for continuous functions
cites work: A homological version of the implicit function theorem
cites work: Discrete maps on manifolds
cites work: Q5528469
cites work: Q5643279
cites work: Q4134602
cites work: Q5522742
cites work: Q5520542
DOI: 10.1016/J.TOPOL.2015.10.013
description: scientific article; zbMATH DE number 6517538